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Algebraic Decoding of Negacyclic Codes over Z4

Eimear Byrne 1 Marcus Greferath 1 Jens Zumbragel 1 Jaume Pernas 2 
1 Claude Shannon Institute
2 DEIC / UAB - Departament d'Enginyeria de la Informacio i de les Comunicacions [Barcelona]
Abstract : We investigate Berlekamp's negacyclic codes and discover that these codes, when considered over the integers modulo 4, do not su er any of the restrictions on the minimum distance observed in Berlekamp's original papers [2, 3]. We present an algebraic decoding algorithm for this class of codes that corrects any error pattern of Lee weight t. Our treatment uses Grobner bases, the decoding complexity is quadratic in t.
Keywords : module of solutions negacyclic code integers modulo 4 Lee metric Galois Ring decoding Grobner bases key equation solution by approximations module of solutions.
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https://hal.inria.fr/inria-00607733
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Submitted on : Monday, July 11, 2011 - 10:23:04 AM
Last modification on : Monday, March 29, 2021 - 11:50:03 AM
Long-term archiving on: : Monday, November 12, 2012 - 10:40:23 AM

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  • HAL Id : inria-00607733, version 1

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INSMI | WCC2011 | TDS-MACS

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Eimear Byrne, Marcus Greferath, Jens Zumbragel, Jaume Pernas. Algebraic Decoding of Negacyclic Codes over Z4. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.101-110. ⟨inria-00607733⟩

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